Oskar Becker, On the logic of modalities (1930) : translation, commentary and analysis / / Oskar Becker, translated by Stefania Centrone, Pierluigi Minari

• Record Nr.: UNINA9910559390203321
• Autore: Becker Oskar <1889-1964, >
• Pubbl/distr/stampa: Cham, Switzerland : , : Springer, , [2022]; ©2022
• ISBN: 3-030-87548-2
• Descrizione fisica: 1 online resource (167 pages)
• Collana: Synthese Library ; ; v.444
• Disciplina: 160
• Soggetti: Modality (Logic)
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Intro -- Preface -- Preface -- Contents -- 1 Introduction -- 2 Part I of On the Logic of Modalities -- 2.1 The Conditional, or The Crows on the Roofs -- 2.2 The Decision Problem and Leibniz's Dream -- 2.3 Normal Modal Logics: a Quick Resumé -- 2.4 Lewis's S3 and Becker's Extensions -- 2.5 Lewis's Survey System S3 -- 2.6 Becker's Six Modalities System S3' -- 2.7 Becker's Ten Modalities System S3'' -- 2.8 Becker's Further ``Experiments'' -- 2.8.1 A Variant of S3' -- 2.8.2 A More Abstract Approach -- 2.9 Becker's Logical Accomplishments: An Assessment -- 3 Part II of On the Logic of Modalities -- 3.1 Introduction -- 3.2 On Edmund Husserl -- 3.2.1 Existence -- 3.2.2 Definiteness and Universal Arithmetic -- 3.2.3 ``To Be Grounded in the Essence of Something'' -- 3.3 On Cassirer and Brouwer -- 3.3.1 On the Object of Mathematics -- 3.3.2 Brouwer's Intuitionism -- 3.4 On Weyl -- 3.5 Oskar Becker on Cassirer -- 4 Oskar Becker: On the Logic of Modalities -- Preliminary Remark -- I. On the Rank Order and Reduction of Logical Modalities -- Introduction -- II. The Logical Interpretation of the Mathematical Intuitionism from the Standpoint of Modality -- Cassirer's Remark on Oskar Becker's Monograph Mathematical Existence172 -- 5 Appendix -- 5.1 Lewis's Axiomatizations of S3 -- 5.2 Lemmon-Style Axiomatization of S3 -- 5.3 Irreducible Modalities in S3 -- 5.4 Kripke-Style Semantics for S3 -- 5.5 Completeness Theorem(s) for S3 -- 5.5.1 Completeness of S3 with ; Respect to Mod2+ and Mod1* -- 5.5.2 Completeness of S3 with Respect to Mod3+ -- 5.6 Finite Model Property and Decidability of S3 -- 5.7 Modal Translation of IPC in S3 and Embeddings of S4 in S3 -- 5.8 Lewis's System S2 -- 5.9 Becker's ``Experiments'': A Technical Evaluation -- 5.9.1 The ``Variant'' Six Modalities System S3* -- 5.9.2 The Ten Modalities System S3'' -- 5.9.3 The System SM -- References.; Author Index -- Subject Index.